Question:
A dealer purchased a fan for Rs 1080. After allowing a discount of 25% on its marked price, he gains 25%. Find the marked price of the fan.
Solution:
Cost price of the fan $=R s 1080$
Gain percentage $=25 \%$
$\therefore$ Selling price $=\left\{\frac{(100+\text { gain } \%)}{100} \times \mathrm{CP}\right\}$
$=\left\{\frac{100+25}{100} \times 1080\right\}$
$=\frac{125}{100} \times 1080$
$=$ Rs 1350
Let the marked price be Rs $x$.
Discount $=25 \%$ of $R s x$
$=\frac{25 x}{100}$
SP = MP − discount
$\Rightarrow 1350=X-\frac{25 X}{100}$
$\Rightarrow 1350=\frac{100 x-25 x}{100}$
$\Rightarrow 135000=75 x \Rightarrow x=\frac{13500}{75} \Rightarrow x=1800$
Therefore, the marked price of the fan is $R s 1800$.